NemoProfile as an efficient approach to network motif analysis with instance collection

A network motif is defined as a statistically significant and recurring subgraph pattern within a network. Most existing instance collection methods are not feasible due to high memory usage issues and provision of limited network motif information.

The Author(s) BMC Bioinformatics 2017, 18(Suppl 12):423

DOI 10.1186/s12859-017-1822-6

NemoProfile as an efficient approach to

network motif analysis with instance collection

From 12th International Symposium on Bioinformatics Research and Applications (ISBRA 2016)

Minsk, Belarus 5-8 June 2016

Abstract

Background: A network motif is defined as a statistically significant and recurring subgraph pattern within a

network Most existing instance collection methods are not feasible due to high memory usage issues and provision

of limited network motif information They require a two-step process that requires network motif identification prior

to instance collection Due to the impracticality in obtaining motif instances, the significance of their contribution to problem solving is debated within the field of biology

Results: This paper presents NemoProfile, an efficient new network motif data model NemoProfile simplifies

instance collection by resolving memory overhead issues and is seamlessly generated, thus eliminating the need for costly two-step processing Additionally, a case study was conducted to demonstrate the application of network motifs to existing problems in the field of biology

Conclusion: NemoProfile comprises network motifs and their instances, thereby facilitating network motifs usage in

real biological problems

Keywords: NemoProfile, NemoCollect, ESU, Systems biology, Biological network, Network motif, Essential protein

Background

Systems biology elucidates, models, and predicts the

behavior of all biological components and their

interac-tions Its emphasis on the interconnections of molecules

produced biological networks as described in Fig 1, where

nodes are molecules and edges are interactions between

them Understandably, various graph theory topics are

substantially applied to resolve various biological

prob-lems, such as prediction of biological function, detection

of protein complexes, discovery of new interactions,

evo-lutionary analysis, information integration, diagnosis of

disease, and drug design [1]

Network motif analysis is one of the graph theory

methods used to find biologically relevant functions in

networks [2] A network motif is defined as an overly

fre-quent and unique subgraph pattern in a network, and it

*Correspondence: kimw6@uw.edu

Division of Computing and Software Systems, School of Science, Technology,

Engineering, and Mathematics (STEM), University of Washington Bothell,

18115 Campus Way NE, 98011-8246 Bothell, WA, USA

has been applied to solve various biological and medi-cal problems: predicting protein-protein interactions [3], determining protein functions [4], detecting breast-cancer susceptibility genes [5], investigating for evolutionary con-servation [6, 7], and discovering essential proteins [8, 9] Furthermore, a broad spectrum of applications has been explored: ‘motif clustering’ [10], ‘motif themes’ [11], ‘rel-ative graphlet frequency distances’ [12, 13], ‘motif modes’ [14], and ‘MotifScores’ [15]

However, identifying network motifs is intrinsically very costly, and this high computational cost restricts extensive and exhaustive experiments for real problems The pro-cess involves enumeration of millions of subgraphs in the input graph, and classification through canonical labeling

or isomorphic testing Then, a network motif ’s unique-ness is established through rigorous statistical testing

in a huge random pool Consequently, various heuristic methods and parallel algorithms have been proposed that alleviate the performance concerns of exhaustive search methods [16]

© The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0

International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made The Creative Commons Public Domain Dedication waiver

Fig 1 Examples of biological networks: a a metabolic network is composed of different types of nodes and edges; b all the nodes in a gene regulatory network are genes, and directed edges represent a regulatory process; c a protein-protein interaction network is composed of proteins,

and their binary interactions are undirected edges

Network motifs may remain meaningless unless their

biological significance is properly evaluated In order to

determine biological relevance, individual motif instances

need to be collected and evaluated in the context of

bio-logical systems However, most motif-finding algorithms

provide only frequency and statistical significance of each

pattern, which restricts its usability for real-world

prob-lems Therefore, we introduce a new network motif

rep-resentation to overcome this problem, and define it as

NemoProfile

In this paper, we show how efficiently NemoProfile

is generated and how this significantly reduces motif

instance collection time We also provide a case study

where NemoProfile is directly applied to the prediction of

essential proteins from protein-protein interaction (PPI)

networks

Methods

Here, we introduce a new network motif representation,

as NemoProfile NemoProfile can be effortlessly

gen-erated while detecting network motifs, and effectively

collects network motif instances We designed and

imple-mented a program based on a flowchart illustrated in

Fig 2 to provide three separate output options:

NemoPro-file, NemoCount, and NemoCollect

NemoCount, which implements ESU (Enumerate

SUb-graphs) algorithm [17], provides the frequency and

statis-tical testing result only NemoProfile and NemoCollect are

described followed by the definition of network motifs

Network motif

Network motifs are defined as frequent and unique

sub-graphs in a network Formally, if G = (V, E) is a graph and

k ranges from 3 to n << |V|, then a network motif m is

a connected subgraph of size k in G, which appears more

frequently than usual In the definition of network motifs,

‘more frequent than usual’ refers to a structural

unique-ness and it is determined by p-value as in Eq (1) or z-score

as in Eq (2) after a number of random graphs have been generated

p-value(m) = 1

N

N



n=1

c(n),wherec(n) =



1, if f R (m) ≥ f G (m)

0, otherwise.

(1)

z-score(m) = f G (m) − average(f R (m))

Here, f G (m) is the frequency of motif m in G and f R (m)

be that of motif in random graph R Also, average (f R (m)) and std (f R (m)) refer to the average and standard deviation

of frequencies in random networks, respectively

Gener-ally, a subgraph with p-value less than 0.01 or z-score

greater than 2.0 is considered as a network motif

Figure 3 describes how to find size 3 network motifs

from the input graph G in the upper left corner by ESU

algorithm [17] The method enumerated a total of 16 sub-graphs of size 3, but one instance, ({1,2,3}), is a triangle type while others are all linear types Although the fre-quency of triangle type is much less than the linear type,

p-value and z-score determine that the triangle type is a network motif Therefore the frequency (or count) of the network motif is 1, and the instance of the network motif

is ({1,2,3}) We want to note that all existing software

pro-grams provide the frequency, and p-value or z-scores of

network motifs but not the instances of network motifs due to heavy memory overhead In this paper, we put more

The Author(s) BMC Bioinformatics 2017, 18(Suppl 12):423 Page 39 of 131

Fig 2 Flow chart of a network motif finding program producing NemoProfile, NemoCollect, and NemoCount(ESU) It searches all subgraphs in a

given network by ‘Enumeration,’ then asks if instances should be collected If yes, all the instances are collected as ‘SubgraphProfile’ form Otherwise the occurrences of each graph pattern is recorded as in the ‘Counting’ step These counts are essential to determine which graph pattern is a network motif as its relative frequency is compared in the random graph pool In the final output, the SubgraphProfile is used to produce

NemoProfile or NemoCollect NemoCount output can be produced without the SubgraphProfile

weight on the importance of network motif instances by

introducing a NemoProfile

Network motif detection algorithms

Various network-motif-finding algorithms are available,

classified into network-centric and motif-centric

algo-rithms [16] Network-centric algoalgo-rithms identify network

motifs while exploring subgraphs in the input graph,

whereas motif-centric algorithms count the instances for each pattern in a predefined query set Then its signif-icance is determined through various statistical testing

in a large random pool to determine network motifs, as summarized in Fig 4

Although network-centric algorithms have the bene-fit that subgraphs that are not in the input graph will never be considered, the inevitable enumeration process

Fig 3 An example of a graph with network motifs and their instances, courtesy of paper [17]

Fig 4 Network-centric methods consists of enumeration and classification, random graph generation, and statistical testing For example, out of six

non-isomorphic subgraphs of size 4 (upper-right table), three patterns at the bottom are determined as network motifs

is heavily expensive Motif-centric algorithms can reduce

classification time if combined with symmetry breaking

or mapping strategies, and can directly verify whether a

specific pattern is a network motif or not [16, 17]

How-ever, the number of non-isomorphic subgraphs (patterns)

increases exponentially with the size of motifs, therefore

even listing them is intractable As an example, there are

11,716,571 patterns for motif size 10, as shown in Table 1

Many motif search programs are also available [18]:

MFinder [19], FANMOD [20], Kavosh [21], Mavisto [22],

Table 1 Number of non-isomorphic subgraphs for undirected

and directed graphs with up to 10 vertices [31]

Vertices Number of non-isomorphic subgraphs

Undirected Directed

10 11,716,571 341,247,400,399,400,000,000

and NeMoFinder [23] follow the network-centric meth-ods Motif-centric methods are available with Grochow’s [24], and MODA [25] However, most of them provide only frequency and statistical significance as in Fig 5, because collecting all instances of each pattern creates

a serious memory overhead problem Hypothetically, the number of subgraphs in the input graph is|E G||Em|where

|E G | is the number of edges in the input graph and |E m|

is the number of edges in motif m [26] That means most

biological networks have several tens or even hundreds

of millions of subgraphs, even for small motifs There-fore, instances of network motifs have to be collected

as post-processing if necessary, and it usually requires more efforts than detecting network motifs, as this step is unavailable with current programs

Considering that most real world problems that use network motifs require a knowledge of what nodes and edges actually belong to network motifs [8, 9], providing their instances will greatly increase the usability of net-work motifs Therefore, the net-work in this paper focuses

on the neglected task in network motif finding, which is collecting instances efficiently and utilizing them for real biological problems

NemoProfile

To reduce computational cost but still provide valuable results, we propose a new network motif representation,

The Author(s) BMC Bioinformatics 2017, 18(Suppl 12):423 Page 41 of 131

Fig 5 The example format of network motif finding outputs, which shows frequency and significance for each pattern

NemoProfile that relates each node to network motifs

as a profile matrix while identifying network motifs As

illustrated in Fig 2, a SubgraphProfile, T as an n × m

matrix is first constructed where n is the number of nodes

in the input graph and m is the number of all subgraph

patterns of size k While enumerating, T ij increments by

1 if a pattern m j includes node v i After network motifs

are determined NemoProfile takes the network motif

columns from T.

For example, we can find 14 instances of “graph78”

size-3-subgraphs and 2 of “graph238” size-3-subgraphs if

a target graph has 9 vertices and 10 edges as shown in

Fig 6a While the Fanmod program that implements ESU

can trace all 16 instances, saving all instances as sets of

vertices, such as,  graph78 = ({1, 2, 4},{1, 2, 5}, {1, 2,

6}, ,{2, 3, 9} ), graph238 =({1, 2, 3}, {3, 8, 9})  causes

a great amount memory overhead Therefore, Fanmod (ESU algorithm) provides the frequencies and statistical results of each type, but discards the motif instances On the other hand, NemoProfile saves the set of instances as

a matrix so that the frequency of each node’s involvement

to each pattern is recorded as shown in Fig 6a Figure 6b describes how to recover the network motif instances

as sets of vertices from a NemoProfile, which generates NemoCollect

NemoCollect

We define NemoCollect as in Algorithm 1 describing the process to collect instances of a network motif m with

NemoProfile It derives an induced subnetwork comprised

Fig 6 The process of collecting instances for graph238: a SubgraphProfile is obtained in the process of ESU from the original input graph in the left From the graph patterns graph78 and graph238, “graph238” is determined to be a network motif through statistical analysis; b NemoProfile (left) is derived from the SubgraphProfile in (a), and effectively identifies an induced subgraph for motif “graph238” by collecting the nodes corresponding

to a non-zero value in the column of graph238 The induced subgraph with nodes 1, 2, 3, 8, and 9 will be processed with EnumerateSubgraph(ESU)

[17] to collect all the instances for graph238

Fig 7 a The chart shows that the running time (Y-axis) to detect size 4 network motifs from various size (number of nodes, X-axis) of PPI networks is very similar with all three options; b This chart compares times of ESU, NemoProfile, and NemoCollect methods while detecting various sizes of

motifs, from size 3 to size 8 NemoCollect takes longer than the other options for larger motif sizes

by all nodes whose m-corresponding column value being

non-negative The subnetwork is fed back to

Enumerate-Subgraph function from [17] to collect the instances of

motif m Figure 6 illustrates the process with an input

graph and NemoProfile

Algorithm 1:NEMOCOLLECT USINGNEMOPRO

-FILE ANDESU [17]

input : Graph G = (V, E), k : motif size,

NemoProfile, motif m

output

:

A set of instances of motif m

1 Let nodeIdVec as a set of the node IDs for

∀node ∈ G do

2 ifnode corresponds to motif m then

3 add to nodeIdvec;

4 Induce a subnetwork S of nodeIdvec

5 Call EnumerateSubgraph (S, k)

6 Output a set of instances of motif m

Results and discussion

We tested the efficiency and effectiveness of NemoPro-file with a number of PPI networks that are available in the DIP database [27] in a Linux operating system, Xeon Core i7 with 5,959 MiB system memory The DIP database includes eight different species of protein-protein inter-action (PPI) networks, which are manually and computa-tionally curated Almost every three months, the networks are updated by adding or removing proteins and their interactions We selected five E coli core PPIs, five S cere-visiae core PPIs, and six H sapiens core PPI networks that are updated each year from 2010 through 2014

We designed and implemented a program by modify-ing ESU with SNAP (Stanford Network Analysis Platform) C++ library [28] to have three separate output options,

‘NemoCount (ESU)’, ‘NemoProfile’, and ‘NemoCollect’ as shown in the bottom box in the flowchart of Fig 2 We should note that the ‘SubgraphProfile’ is an intermedi-ate datum to generintermedi-ate ‘NemoProfile’ and ‘NemoCollect’ at the end

Fig 8 a This chart shows that NemoCollect takes significantly less time compared to AllCollect and QueryCollect, while collecting size 4 motif instances from various inputs; b It shows that AllCollect takes up significant time compared to other methods, and that NemoCollect method is the

most efficient when collecting size 5 motif instances

The Author(s) BMC Bioinformatics 2017, 18(Suppl 12):423 Page 43 of 131

Table 2 Running time (in seconds) of NemoCollect, QueryCollect

and AllCollect with various motif sizes, as in Fig 8b

E:size3 S:size3 E:size4 S:size4 E:size5

NemoCollect 5.56 27.86 61.74 348.01 1768.40

QueryCollect 11.18 54.14 117.45 655.04 2504.40

AllCollect 17.74 159.53 2405.90 131.49 170,420.00

NemoCollect is the most efficient, while AllCollect becomes intractable with motifs

of larger sizes

Performances of NemoProfile and NemoCollect are

compared with NemoCount in various testing scenarios

by varying the size of the input graph, or by varying the

size of network motifs to detect Figure 7a demonstrates

NemoProfile and NemoCollect take almost the same time

as NemoCount(ESU) for size 4 network motifs in

vari-ous input graph sizes Time for detection of varivari-ous sizes

of network motifs is also compared in Fig 7b Inevitably,

NemoCollect takes slightly more time than others as the

size increases due to the additional instance collection

time However, time of NemoProfile is still similar to that

of ESU proving that it is efficiently generated but contains

much richer information than ESU

Next, we wanted to see if NemoProfile significantly

alleviates the memory overhead problem when

collect-ing network motif instances We design “NemoCollect”

process as shown in Algorithm 1 which uses

NemoPro-file in the process Since none of the existing network

motif finding algorithms collect network motif instances,

we designed a couple of alternatives to compare them with

NemoCollect: AllCollect is collecting all subgraphs while

searching network motifs, and QueryCollect is

collect-ing the instances of motifs uscollect-ing motif-centric method

Although the time of AllCollect is directly measured, the

time for QueryCollect method is estimated, assuming that

it will run ESU first to determine network motifs and

run MODA later to collect the instances of the network

motifs Since MODA takes as much time as ESU,

accord-ing to paper [25, 26], we estimated the time for

QueryCol-lect as twice that of ESU Figure 8a and b demonstrate

that NemoCollect is the most efficient method for motif

instance collection, even with an increase in motif size

Table 2 supplements Fig 8b to show the differences

clearly

Case study: essential protein prediction and NemoProfile

This section demonstrates the usability of NemoPro-file for real-world applications, specifically predicting essential proteins in a PPI network where network motif analysis has been applied previously [8, 9]

We used E coli (‘Ecoli20101010CR’) and S cere-visiae (‘Scere20101010CR’) PPI networks from DIP, and

obtained the list of essential proteins from Database of essential genes (DEG)[29] E coli has 121 essential pro-teins out of 1,231 nodes, and S cerevisiae contains 782 essential proteins out of 2,200 proteins

First, NemoProfile program provides the NemoProfile

matrix (A) of each network where the number in A ijrefers

the number of protein i overlaps with a motif j Here, five

network motifs are identified in both of the networks, and NemoProfile structure is directly converted to the set of attributes for each protein The data attributes along with the protein’s essentiality is fed into Weka program [30]

to run a decision tree (J48) algorithm to predict essential proteins

Figure 9 summarizes the overall process, from a PPI net-work, through NemoProfile, and the application of the decision tree technique to predict essential proteins of

an organism The classification is evaluated using 10-fold cross-validation scheme, and Fig 10 is one example of Weka results on S cerevisiae PPI

Conclusions

Several computationally costly tasks are required for net-work motif finding since netnet-work motifs are unique both structurally and statistically These tasks include enu-meration, classification, and statistical analysis Network-centric and motif-Network-centric methods exist for finding motifs While these methods have reduced computational costs, they have not overcome the prejudice towards network motifs in problem solving The doubtfulness as to the rele-vance of network motifs in biological problems continues due to the lack of usability with existing programs Therefore, we emphasized their usability by present-ing NemoProfile, an efficient network motif represen-tation Significant improvement is seen with the mem-ory overhead problem resolution and the reuse of NemoProfile to collect instances of motifs for direct appli-cation to existing problems Additionally, NemoProfile provides the output from other representations, including

Fig 9 Process to predict essential proteins in a PPI network A PPI network is processed to obtain NemoProfile matrix (A) that shows protein i has A ij

overlaps with motif j The matrix is directly loaded into a Weka program to run a decision tree algorithm and is evaluated through 10-fold

cross-validation method to provide prediction rate and ROC area value as a result

Fig 10 Result of prediction of essential proteins with Weka, detected from S cerevisiae

the frequencies and statistical significance of subgraph

patterns

A NemoProfile program was constructed and used

to demonstrate the effectiveness of network motifs in

application to real world problems The experiment was

conducted using PPI networks and the results showed

that NemoProfile succinctly represents network motifs

and their instances with no extra computational costs

incurred With a favorable outcome in comparison with

other alternative methods NemoCollect is defined as the

process of collecting instances from NemoProfile The

outcome clearly demonstrates that the performance is

sig-nificantly better than the alternatives A usability focused

case-study of NemoProfile was performed to predict

essential proteins in PPI networks According to the study,

the application of machine learning algorithms can be

eas-ily applied to NemoProfile by first converting it to data

feature space

Future works on NemoProfile include three main tasks

First, the design of a framework to enhance the

applica-tion of NemoProfile to current and future problems, thus

reducing prejudice towards network motif analysis in the

field of biology Second, enhance the NemoCollect process

using parallelization by leveraging each separate column

in NemoProfile Third, improve the NemoCollect process

using a symmetry breaking or mapping process

Abbreviations

DEG: Database of essential genes; DIP: Database of interacting proteins; ESU:

Enumerate SUbgraphs; NemoCollect: Network motif instance collection;

NemoCount: Network motif count; NemoProfile: Network motif profile; PPI:

Protein-protein interaction; SNAP: Stanford network analysis platform

Acknowledgements

The authors would like to thank the University of Washington Bothell for

supporting this research program.

Funding

Publication of this article was funded by the school of STEM at the University

of Washington at Bothell (UWB), which played a role in the design of the study

by providing an interdisciplinary research environment.

Availability of data and materials

The NemoProfile source and documentation is available at http://faculty washington.edu/kimw6/research.htm The datasets during the current study are available in the DIP (the Database of Interacting Proteins) [27] repository.

About this supplement

This article has been published as part of BMC Bioinformatics Volume 18

Supplement 12, 2017: Selected articles from the 12th International Symposium

on Bioinformatics Research and Applications (ISBRA-16): bioinformatics The full contents of the supplement are available online at https://bmcbioinformatics biomedcentral.com/articles/supplements/volume-18-supplement-12.

Authors’ contributions

WK conceived of the study, designed and tested the methods, and wrote the manuscript LH conceived of the study, implemented the methods, and wrote the manuscript All authors read and approved the final manuscript.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Published: 16 October 2017

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